To solve the problem, we start by examining the given equation of the circle: [tex]\( x^2 + y^2 = 100 \)[/tex]. This equation represents a circle centered at the origin [tex]\((0,0)\)[/tex] with a radius squared of 100.
1. Identify the radius of the circle:
The equation [tex]\( x^2 + y^2 = 100 \)[/tex] can be compared to the standard form of a circle's equation [tex]\( x^2 + y^2 = r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius.
Here, [tex]\( r^2 = 100 \)[/tex]. To find [tex]\( r \)[/tex], we take the square root of both sides:
[tex]\[
r = \sqrt{100}
\][/tex]
[tex]\[
r = 10
\][/tex]
Thus, the radius of the circle is 10 inches.
2. Calculate the diameter of the circle:
The diameter of a circle is twice the radius. Therefore, we multiply the radius by 2:
[tex]\[
\text{Diameter} = 2 \times \text{radius}
\][/tex]
[tex]\[
\text{Diameter} = 2 \times 10
\][/tex]
[tex]\[
\text{Diameter} = 20
\][/tex]
So, the diameter of the cushion is 20 inches.
Therefore, the correct answer is:
[tex]\[
\boxed{20 \text{ in.}}
\][/tex]
